I am aware that the spectral radius is bounded above by the 2-norm of the matrix, that is $\rho(A) \le \|A\|_2$ where $\rho$ is the spectral radius.
Does there exist a result such that $\|A\|_2 \le C \rho(A)$ for some known constant $C$?
I'm only concerned about real-valued matrices $A$.